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Digital filter banks have found in a wide variety of applications in data compression, digital communications, and adaptive signal processing. The common objectives of the filter bank design consist of frequency selectivity of the individual filters and perfect reconstruction of the filter banks. The design problems of filter banks are intrinsically challenging because their natural formulations are nonconvex constrained optimization problems. Therefore, there is a strong motivation to cast the design problems into convex optimization problems whose globally optimal solutions can be efficiently obtained. The main contributions of this dissertation are to exploit the convex optimization algorithms to design several classes of the filter banks. First, the two-channel orthogonal symmetric complex-valued filter banks are investigated. A key contribution is to derive the necessary and sufficient condition for the existence of complex-valued symmetric spectral factors. Moreover, this condition can be expressed as linear matrix inequalities (LMIs), and hence semi-definite programming (SDP) is applicable. Secondly, for two-channel symmetric real-valued filter banks, a more general and efficient method for designing the optimal triplet halfband filter banks with regularity is developed. By exploiting the LMI characterization of nonnegative cosine polynomials, the semi-infinite constraints can be efficiently handled. Consequently, the filter bank design is cast as an SDP problem. Furthermore, it is demonstrated that the resulting filter banks are applied to image coding with improved performance. It is not straightforward to extend the proposed design methods for two-channel filter banks to M-channel filter banks. However, it is investigated that the design problem of M-channel cosine-modulated filter banks is a nonconvex optimization problem with the low degree of nonconvexity. Therefore, the efficient semidefinite relaxation technique is proposed to design optimal prototype filters. Additionally, a cheap iterative algorithm is developed to further improve the performance of the filter banks. Finally, the application of filter banks to multicarrier systems is considered. The condition on the transmit filter bank and channel for the existence of zero-forcing filter bank equalizers is obtained. A closed-form expression of the optimal equalizer is then derived. The proposed filter bank transceivers are shown to outperform the orthogonal frequency-division multiplexing (OFDM) systems.

Typescript (Photocopy) / Bibliography: leaf 75 / 75 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1985?

Typescript (photocopy) / vi, 151 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1982

We describe our overall approach to building robot vision systems, and the conceptual systems architecture as a network of agents, which run in parallel, and cooperate to achieve the system’s goals. We present the current state of the 3D Feature-Based Tracker, a robot vision system for tracking and segmenting the 3D motion of objects using image input from a calibrated stereo pair of video cameras. The system runs in a multi-level cycle of prediction and verification or correction. The currently modelled 3D positions and velocities of the feature points are extrapolated a short time into the future to yield predictions of 3D position. These 3D predictions are projected into the two stereo views, and are used to guide a fast and highly focused visual search for the feature points. The image positions at which the features are re-acquired are back-projected in 3D space in order to update the 3D positions and velocities. At a higher level, features are dynamically grouped into clusters with common 3D motion. Predictions from the cluster level can be fed to the lower level to correct errors in the point-wise tracking.

Thesis (Ph. D.)--Virginia Polytechnic Institute, 1975. / Also available via the Internet.

Thesis (Ph. D.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 155-165) Also available in print.

Thesis (B.A.)--Haverford College, Dept. of Mathematics, 2002. / Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 155-165) Also available online.

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Title from PDF of title page (University of Missouri--Columbia, viewed on March 29, 2010). Thesis advisor: Dr. Alexander Koldobsky. Vita. Includes bibliographical references.